What a difference three months make. As Mark Carney was gearing up in February for his third inflation report as Bank of England governor, life in his new city must have looked pretty overcast.

Most of us feel that way after the long slog of a British winter and it is little different in Carney's native Canada. But for the man known back home as the "rock-star central banker", this particular February brought a daunting appointment with the press.

A mere six months after introducing "forward guidance" – to great fanfare – Carney was preparing to admit to a throng of journalists that he would be watering down his key policy.

Jump ahead three months to May and the skies are bluer. At this week's inflation report, Carney can claim with quite a bit more credibility that forward guidance, and an implicit vow to keep interest rates at their record low for a long time to come, have helped boost business confidence and supported the recovery. Unemployment fell below the 7% threshold that was enshrined in the first version of the policy far earlier than the Bank had predicted, but even as forward guidance phase one went out the window, expectations over the timing of the first rate rise shifted fairly little.

But for Carney and his colleagues on the monetary policy committee, new challenges are emerging and they are much trickier than a bit of awkwardness over the UK's falling jobless rate. The Bank's decision to leave borrowing costs at their record low of 0.5% last week – as predicted by everyone – was rightly eclipsed by far more interesting goings-on at the European Central Bank.

Grappling with low eurozone inflation and a strengthening currency, ECB chief Mario Draghi was all but certain that policy in the eurozone would be loosened next month. The man who vowed in 2012 to do "whatever it takes" to save the euro had more strong words for the markets. He asserted the ECB was "comfortable" with acting in June, barring any surprises in the inflation projections. At the same time, Federal Reserve chief Janet Yellen reaffirmed that the US central bank would maintain its ultra-supportive policy for some time yet.

So the ECB is getting ready to put its foot on the gas and the Fed is telling us it will be sticking in the fast lane while the Bank of England is being told to test the brakes.

Against the backdrop of accelerating house prices and other assets taking off, some economists are predicting action from the Bank this year. Others disagree and look to the end of 2015. But they do concur on one thing: when the move comes, it will be upward. That leaves Britain with a strongly diverging interest rate outlook from its main trading partners and brings two big problems for UK policymakers.

Firstly, the contrast could serve to inflate asset bubbles that monetary tightening would have been hoped to constrain. Expectations of negative interest rates in the euro area – which effectively means bondholders pay for the privilege of holding government debt – may well trigger capital flows into the UK, as investors search for better returns here that will further inflate asset prices across the board.

The second problem is the likely boost to an already appreciating pound. Carney and George Osborne say they want to see a more balanced recovery, but a strong pound poses a threat to exports. Sterling climbed against the euro on Draghi's comments and against the dollar it was trading at around five-year highs last week.

Carney and his colleagues will be reluctant to be seen to be moving significantly far ahead of the US. At the same time, they will have to navigate through the ECB's potential easing.

Of course, Bank policymakers will stress when talking on the record that their mandate is to target inflation at 2% and that is how they set rates. But let's face it, in a small open economy, inflation is also heavily influenced by the exchange rate, import prices, and particularly global energy prices.

After inflation hit a peak of 5.2% in September 2011, then governor Lord King was careful to highlight those forces at the time as he warned of an uncertain path ahead. "Much of that uncertainty stems from events beyond our shores and over which the monetary policy committee has little influence. In such circumstances, there are limits to what domestic monetary policy can achieve," he said.

But when it comes to popping bubbles, the Bank's powers are limited too. On house prices particularly, observers such as the Organisation for Economic Co-operation and Development are wrong to look to the Bank for solutions. It is not a housing bubble, it is a housing crisis, and only building more homes will fix it, not changes to interest rates.

The inconvenient truth for the MPC is that it is unable to prevent asset-price bubbles when other central banks are pumping the world full of liquidity. Osborne may have hired a rock-star banker, but Carney's ability to deliver is much more limited than we would like to think. Add in political uncertainties at home and rising tensions in Ukraine, and those blue skies look like they are clouding over again.